Optimization of Inventory and Distribution for Hip and Knee Joint Replacements via Multistage Stochastic Programming
We introduce a multistage stochastic programming model to optimize the distribution–production network of medical devices; in particular, artificial hip and knee joints for orthopedic surgery. These devices are distributed to hospitals in kits that contai
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Abstract We introduce a multistage stochastic programming model to optimize the distribution–production network of medical devices; in particular, artificial hip and knee joints for orthopedic surgery. These devices are distributed to hospitals in kits that contain multiple sizes of the joint; the surgeon uses one device from the kit and then returns the rest of the kit to the distributor, which replaces the part that has been removed and distributes the kit anew. Therefore, the distribution problem for artificial joints has a shareability property and thus is related to closed-loop supply chains. We assume that demands for the devices follow a discrete probability distribution and therefore we use scenarios to model the random demands over time. We compare the results of our optimization model to an approximation of the simple distribution strategy that our industry partner currently uses. The proposed approach outperforms the present approach in terms of optimal cost. We also explore the sensitivity of the model’s computation time as the numbers of scenarios, hospitals, and time periods change. Finally, we extend the model to investigate the production of shareable items in sharing systems using a numerical example. Keywords Hip and knee joint replacement logistics · Sharing systems Production–distribution planning · Multistage stochastic programming Healthcare systems
M. Pirhooshyaran (B) · L. V. Snyder Mohler Lab, Department of Industrial and Systems Engineering, Lehigh University, 200 West Packer Ave., Bethlehem, PA 18015, USA e-mail: [email protected] L. V. Snyder e-mail: [email protected] © Springer Nature Switzerland AG 2019 J. D. Pintér and T. Terlaky (eds.), Modeling and Optimization: Theory and Applications, Springer Proceedings in Mathematics & Statistics 279, https://doi.org/10.1007/978-3-030-12119-8_7
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M. Pirhooshyaran and L. V. Snyder
1 Introduction The last two decades have witnessed a dramatic increase in the number of hip and knee replacement operations around the world. Both are currently among the most common orthopedic surgeries. Aimed at improving the functionality and quality of life of patients, more than half a million knee and hip replacements are performed in the United States annually. Considering that population aging and obesity are both on the rise, the requests for joint replacement operations are predicted to exceed two million by the end of 2025 [19, 45]. On the other hand, the average cost of a total joint replacement is up to $40,000 in the United States and around $12,000 in the majority of European countries. The total cost of the components to be used in a joint replacement surgery can be up to $5,000 [31, 40]. It is common in the orthopedic industry for device manufacturers, or third-party distribution companies, to own and maintain the inventory of the devices. Typically, most of the inventory is either located at a hospital for use in a surgery in the near future, or in transit to or from the distributor’s warehouse or from one hospital to another; very little in
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